Method and means for finding geographical position in navigation



Oct. 20, G. W. LITTLEHALES METHOD AND MEANS FOR FINDING G'EOGRAFHICAL POSITION IN NAVIGATION 192! Sheets-Sheet Fil 0a. 2o, 1925. A 1,557,854

G. W. LITTLEHALES METHOD AND MEANS FOR FINDING GEOGRAPHICAL POSITION IN NAVIGATION Filed Sept. 30. 1921 5 Sheets-Sheet 2 lumen/tom Oct. 2o, 1925.

G. W. LITTLEHALES METHOD AND MEANS FOR FINDING GEOGRAPHICAL POSITION IN NAVIGATION mselp-SO 1921 3 Sheets-Sheet 5 gwn/Mo odjv Q/ 3542? L; 'y www Patented Oct. 20, 19,25.

UNITED STATES PATENT oFF-lcs.

GEORGE W. LITTLEHALES, 0F WASHINGTON, DISTRICT 0F COLUHBIA.

Application led September 30, 1921. Serial No. 504,480.

Toallfwhomz'tma concern:

Be it knownV t at I, GEORGE W. Lima- HALE, a citizen of the United States, residing at 2132 Leroy Place NW., Washington, District of Columbia, have invented certain new and useful Improvements in Methods and Means for Finding Geographical Position in Navigation, of which the following is a specification.

This invention relates to methods for finding geographical osition in navigation by observations of ce estial bodies.

It is the rincipal object of the invention to aifordp an improved method by which Vposition may be found more quickly and with less mental eiicrt than has been possible in the past. Aside from usefulness in marine navigation, this method is `especially adapted for use in aerial flight, wherein conditions obtain which make position finding a more diliicult problem than in the former branch of navlgation.

According to methods heretofore employed in arine navigation, such as Sumners methrli for instance, it has been necessar to make more than one observation of a c osen celestial body and to separate these observations by a considerable length of time. It has been `necessary to `remain immobile btween observations, or to measure very accurately the extent and direction of movement, when compelled to continue on the course. These conditions can be satisfied in marine navigation, wherein the ship on which the navi ator is sailing can be stopped or sailed on a definite course for a determinable distance. In aerial Hight, however, a cruising aircraft cannot suspend its motion, nor is it. practicable to y over a definite, measured course under conditions which make astronomical observations necessary in position ndin A further olgject in view is the provision of a chart designed to facilitate practice of the improved method. It' is intended that this chart shall bear a dia ram and certain data which will enab e the navi ator to follow the method without having to make tedious calculations. A pilot has to focus his attention on so many thin in the performance of his usual duties t at a position finding method involving numerous mathematical computations would be burdensome and impracticable.

The improved method is based upon the principle that at any instant of time there 1s a series of ositions on the earth at which a celestialP body appears at the same given altitude and that these positions lie 1n the circumference of a circle marked out by a radius arm whose pivot is that geographical position which has 'the body in lts zenith and whose len h is the same arcmeasure as the zenith distance or the com-` plement of the altitude. ceeds to recognize that the difference of the simultaneous altitudes of the same celestial body at two geographical positions is the shortest great circle arc-distance between the circles of equal altitude passing throu h the two places. altitudes and azimuths of the celestial bodies as they would appear at stated intervals of time in a chosen geo raphical osition within the limits of the c art, an o server, in a position as yet unknown, having measured the altitude of a celestial body, may at once lay down the locus of his position by comparing the altitude so measured with the tabulated altitude of that body and layin oft' the di'erence between the measured an tabulated altitudes as an intercept from the chosen geographical position in the direction of the azimuth of the celestial body and toward or away from the bearing of the body according as the measured altitude waas higher or lower than the tabulated altitu e.

It is proposed to construct a chart for the geographical area that is to be traversed in any particular cruise or aerial flight. This chart will include a map of the area, a record of the altitudes and azimuths of various celestial bodies as observed from a selected known position on the* map at stated The method prointervals of time, and a diagram the use of which the altitude-difference intercept mag be laid oif readily.

y way of concrete exam idea ma be expressed in t e method steps specifie in the followin description and in the specilic form of c art illustrated in the accompanying drawings, in which:

Figure 1 is a plan view of a chart con le, the inventive By supplying the structed for aerial flight over the central part of the United States of America, showlng loci marked thereon in finding position at two points within the re resented area;

Figure 2 represents a sp erical triangle showing the parts whose relation is expressed in the fundamental equation (e uation (1) page 4 of the following speci cation F1) re 3 represents the method of showing t e relation of the parts shown in Figure,2 and in the fundamental equation with reference to Cartesian rectangular coordinate whose abscissae and ordinates are the haversines of angles ranging from 0 to 180;

Figure 4 is of like nature with Figure 3, hein an ex ression of equation (4) page a, w creas igure 3 is an expression of equation (3), same page;

Figure 5 re resents the first quadrant of the system o Cartesian rectangular coordinates with the ordinates drawn from the points 0f subdivision of the scale of haversines of angles, ranging from 0 to 180, on the axis of abscissee 0 and also on the axis of ordinates, OY;

Figure 6 is intended to illustrate the use of the construction shown in Fi ure 5 for ,the lpurpose of finding the altitu e and azimut o a celestial body, "to-be employed in combination with the chart shown in Figure 1.

r Figure 7 is a plan view of a template for use in drawing the circumferences of circles of equal altitudes.

In order to make clear the fundamental rinciples underlying the invention and to illustrate its practical application to some branch of navi ation, the construction and use of a chart or an aerial flight over the central part of the United States will be considered.`

It may be Well, at this point, to define a few of the terms used in the specification.

and claims. Foi` instance, chart is employed to designate the sheet, tablet. or other member having a surface on which the map, tabulated measurements, diagram', or a substitute for the tabulated measurements` such as the supplementary diagram described later in the specification, or any other parts of the entire organization of lines and indicia, are delineated. That part of the organization which is a conventional representation of part of Ythe earths surface has been termed the map The diagram is'the ,s stemof lines overlying part of the map w ich facilitates determination of position when certain preliminary data has been obtained.

Referring to-Figure 1 of the drawings, the numeral 5 designates the chart, which may be of any suitable type or form. A at chart has been selected for the purposes of disclosure. The geographical area to be traversed is'represented on the face of the chart b map 6. In the case of a iiat chart, t e map should be constructed upon a system of projection having such qualities that angles are preserved nearly true, that the great circle is practically a strai ht line, and that there is uniformityv of sca e within the required limits of tolerance. Zenithal projection is considered to be the most suitable for this purpose, but polyconic, or any other system which possesses the qualities enumerated, may be utilized.

It being assumed that the flight is to be made over the central part of the represented area, some known position in the middle of the map is selected as a reference point, and a record is lnade of the simultaneous altitudes and azimuths of certain celestial bodies as measured by an observer stationed in the selected position at regular intervals of time. Intervals of 4 minutes of hour angle from the observers meridian are suitable for this purpose. Besides the altitudes and azimuths of the brighter stars, the record should embrace the range of the declination, both north and south of the equator, of the sun, the moon, and the planets.

Table 7, in Fig. 1, is an extract from the complete record which might be obtained of measurements made in latitude 39 and longitude 97, which has been chosen for the reference point in this example. On this table, while the azimuth is stated in degrecs and tenths of a degree, the altitudes are set down in degrees and minutes, since the minute of altitude corresponds closely with the geographical mile. Future experience is relied upon to dictate Whether the altitude should be expressed in degrees and decimals of a degree instead of degrees and minutes.

A large compass diagram 8, consisting of radial lines 8 graduated in degrees of azimuth has been delineated on the map with its center at the reference point in latitude 39 and longitude 97. since all the altitude differences are to be laid off from there; and circumferences 9 concentric to this point have also been supplied, in order that, with a given altitude-difference` the ohserver may 'at once proceed to find the point through which his line of position is to be drawn, by passing out by the amount of the altitude-difference to the proper los drawn or intermediate circumference along isc neuneu simultaneous altitudes of Tauri (Aldeharan), bearing Westward, and a: Leonis (Regulus), bearingl eastward. By horizonfree sextant true altitude of a Tauri, 55 35 and of a: Leonis 35 13.

Find the geographical position of the observer.

Solution:

a aun i a Looms (Regulus).

`h. m. a. h. 1n. a. Local Sldereal time 6 59 14 6 59 14 Right ascension 4 3l 12 l0 04 00 Hour angle 2 ze o2 3 4 4s with these hour angles entering the tabulation on the chart under the names of these stars.` Az. N. 114 .5 W. N. 110 .1 E.

Alt 50 34 41 19' Measured altitnde 55 35' 35 13' Altitude-dieren 5 0l301 6 0'366' In direction- In direction- N. 114 .5 W. nr (1B0+110 .l)-290 .1 0r S. .5 W. N. 69" .9 W.

The right ascension of each star is obtained by reference to a Nautical Almanac covering the date of observation.

The osition-lines, or loci, resulting from these o servations have been plotted on the map by passing out to the distance circumference 301 01') along the radial N. 114 .5 1V. and through the point thus arrived at, drawing the position-line AB at right angles to the radial; and, likewise, by passing out to the Adistancecircumference 366 (=6 06') along the radial N. 69 .9 W., and through the point thus arrived at, drawing the position-line CD at right angles to this radial. The intersection of these position-lines fixes the geographical position approximately over the city of Denver in latitude 39 45 N. and longitude W. i

To amplify the illustration, a secondexample is presented as follows:

Examplez-An observer in aerial tiight along the coast of the Gulf of Mexico, during the morning of October 14, 1917, measures the true altitude of the suns center to be 40 14 at 9 h. 06 m. 06 s. a. In. b' a watch regulated to mean time of the merid)- ian 97, or 6 h. 28 m. West of Greenwich. From the-Nautical Almanac, the equation of time and suns declination at time of observation are ascertained to be:

Eq.T.=l3 m. 54 s. to mt., Dec. 8 5 .4 S.

Find the position line upon which the observer is located, and, by noting the intersection of this line with thecoast line, the observers geographical position. i i h. m. s.

amr-9 os Eq. T. 13 54 Laar. e zo `au n. A. -2 4o Dee, -s .a 4

Entering the tabulation on the chart with these values c! the H. A. and Dec. ...L...... Az. 132 .7

Alt. 31D" M A It. 42 16 direction N. 132 .7 E.

Passing out to the distance 732 along the radial N. 132 .7 E.. and drawing a position-line IK at right angles to the radial. locatesthe aircraft on the coast a little to the eastward of Pensacola.

Under self-imposed restrictions adopted in consideration of the circumstances and limited equipment of the aerial navigator, a solution of these observations for geographical position has been reached that is without the defaults which arise from treating the great circle arc of altitude-differenceas a rhumb-line, and the exactitude with which the result has been reached would, if the scale of the chart `had not been reduced, be suicient to meet the requirements of aerial navigation. T-he availability of charts of like design will also prove etlicient in meeting the required greater exactitude of marine navigation. if, instead of drawing the line of position as a straight line. the actual curve of the circle of equal altitudes be emplo'ed. This has the curvature on the present c art of a parallel of latitude representing a latitude equal to the altitude of the celestial body observed to obtain theL circle of equal altitudes.

'In this manner, the actual curves EF and GH for which the straight lines AB and CD were substituted have been supplied by the side of them so that a comparison may be made, in the ease in point, between tht` position indicated by the intersection of AB and VCD and that obtained by the intersection of the arcs of the actual circles of equal altitudes.

Attention should perhaps be drawn to the factthat, although it may not be found inconvenient to consult a complete set of tables in actual flight, it is better to ex tract portions for any particular flight, as has been done for the solution of the foregoing problems. Of course, it will not be overlooked that these tables would. without modification, serve a likepurpose in relation to a similar chart of any other part of the world traversed b v the 39th degree parallel of latitude` either in the Northern or Southern Hemisphere.

` Having described the general nature of the method, means for facilitating its practice, and the use of both in solving two concrete problems in position finding, the method may analyzed into the following steps:

1. Measurement of the altitude of one or more visible celestial bodies at a definite instant of time by the observer at the unknown position to be located;

2. Determination, by reference to a chronometer and to recorded data, of the time of observation, the right ascension, and the altitude and azimuth of each body at a known position at the time of measurement of the altitude at the unknown position;

3. Calculation of the difference between the altitude of each bod; at the known positionand that at the un nown position;

4. Locating on a map, in the case of each body, a point spaced from the known position in the direction of the azimuth at a distance representing the altitude difference; and

5. Delineation on the map of a positionline through each of the said points atV right angles to the corresponding azimuth and of such length that each will intersect the YLacasse other, or some representedgeographical feature which is visible to the observer, to locate the unknown position.

The foregoing analysis is general enough to cover observations of a plurality of celestial bodies at night, when they are visible, and also observation of the sun in the daytime. when it alone can be seen. Examples 1 and 2 involve both of these situations and show the slight modifications in the Imethod necessary to meet these different situations.

In order to reduce further the time and mental effort required in finding position according to this method, a graph has been devised which enables the observer to determine altitude, azimuth, or hour-angle, without making extensive mathematical calculations or referring to tabulated data. This sup lementary graph is based on a formula or finding the zenith-distance in which the haversine is the only function employed. (See page 157 American Practical Navigator, N. S. Hydro aphic Oiiice Publication No. 9, Edition o 1920.) (See polar triangle in Fig. 2.) The formula may be state in the form but may perhaps be made appear in more familiar terms by employing the symbols for latitude, L, and declination, d, instead It may be re-written for computing a time-sight or hour-angle, thus:

hav z-hav (L-d) of those for co-latitude, co-L, and polar distance, PD, as follows:

hav z-hav (Co-L-PD) (hav (Co- L.+PD) -hav (Co-L-PD) )hav t, (5)

it is evident that, when the observed celestial body is on the upper branch of the meridian of the observer, that is, when t is equal to zero,the right-hand member of the nation reduces to zero since the haversine o 0 is equal to zero, and therefore,

hav z=hav (Co--L-PD) :0

hav e=hav (Co-L-PD) (6) which is equivalent, as it should be, to the usual statement of the formula for finding im (co-L+PD) im (co-L-Pm since the haversine of V180 is equal to unity, and therefore,

hav z-hav (co-L-rnyhv (co-L+PD) hav (co-L PD) (7) hav z=hav (Ce-L-i-Pm which is equivalent to the usual statement of the formula for finding the latitude from the meridian altitude of a celestial bod culminating below the elevated pole of t e observer.

i Employing Cartesian rectangular co-orditersecting the axis of Y at a distance a above the origln andpassing through the first quadrant at 'an angle of inclination to the axis of X whose tangent is m.

If the axes of Y and X be graduated on the same scale to represent the haversines of angles, commencing with 0 at the origin designated by the letter O in Fig. 3, and extending to 180 in each case, the line EF will be the graph of the equation ya=mw, and hence of The length of the ordinate to the line EF, corres onding to any given value of t on the sca e, OX, of abscissae representing the values of t, will mark the value 0f z on the scale OY of ordinates representing the values of hav a; and conversely, the abscissa corresponding to an given value of z (as when the altitude o a celestial body is measured in taking a time-sight) on the scale of ordinates, OY, will mark the value fjhe hour-angle, t, on the scale of abscissae, In like manner, equation (4) for finding the azimuth, Z, in which Z appears in the f place of t, and the altitude, li, in place of the declination, d, may be represented by a straight line whose rectangular co-ordinates, as represented in Fig. 4` `are hav Z and hav (90 -d), respectively, and whose inclination to the axis of abscissac in hav Z is an angle Whose tangent is equal to and OY and thus forming a grillage of rec-` tangles as shown in Fig. 5.

If the right-hand border of the grillage be numberedln the reverse order from the lefthand border, that is, from 180 at the bottom to 0 at the top, the right-hand ordinate will be L-f-d in findin the hour-angle and t-he zenith-distance, and L-[JL in finding the azimuth, instead of 180- (L-l-d) and 180`-(L+h) as indicated in Figs. 3 and 4 in these respective cases. Hence the following rules, by which an illustrative exam le given below is solved upon the finished a titude and azimuth diagramtof Fig. 6 may be laid down for solving the azimuth and altitude or zenith-distance for finding the position-line by the Saint Hilaire method, and also the time-sight with a degree of precision governed b the scale of construction.

(1) To d the azimuth (Z). Mark the value of (L-h) on the left-hand scale, and the value of L-i-h on the right-hand scale.

Connect these two markings by a straight line. Mark the intersection of this line with the horizontal line from the value of the polar distance (90-d) found on the lefthand scale. The vertical line from this intersection will mark, on either the top or the bottom scale, the value of Z.

(2) To lind the zenith-distance (e) mark the value of (L d) on the left-hand scale, and the value of L-l-d on the right-hand scale. Connect these two markings by a straight line. Mark the intersection of this line with the vertical line from the value of the hourangle (t) found on the top or bottom scale. The horizontal line from this intersection will mark on the left-hand scale, the value o a.

(3) When the altitude,. and hence the zenith-distance, is known byr measurement, by reversing the last two steps in rule 2, the hour-angle may be found.

In order to illustrate the use of the graph the following noblem in determination of altitude and azimuth may be solved:

Example Given hour-angle, t=5 h. 1 m. 17 s.

Find the altitude and azimuth.

Solution:

On the grillage of Fi 6 by rule 2, plotting L-d==.28 on t e left-hand border scale and L+d=20 16 on the right-hand border scale and connecting these two points by a straight line (which is represented on the diagram by short dashes but which need not be drawn in ractice if a` ruler be laid, or a cord be stretc ed, between the points on the border scales), the ordinate on the lefthand scale corresponding to the absissa t=5 h. 1 m. 17 s. is indicated to be 84 54', which is the zenith-distance, z. Hence the altitude, h=a=5 6.

Having now found the altitude, b rule 1, plot L-h=27 46 on the left-han scale and L+h=37 58 on the right-hand scale and connect these points by a straight line (which is represented on the diagram byv long dashes). The abscissa on the top or the bottom scale corresponding to the ordinate,

` cation 10 is place PD--d 102 36'I on the left-hand scale, is indicated tobe 108 35', which is the azimuth counted from the north.

The sup lementary diagram, when substituted for t e tables, should make it possible for an aerial navigator to nd his position even more quickly than by use of the tables. He has with him the equivalent of a volume on nautical astronomy in a form sim le enough to fulfill the instant needs of ig t.

In Figure 1, the diagram of circles of equal altitudes and compass bearings covers only a limited area. Should the navigator happen to pass outside the area. represented by this diagram, the circumference of an additional circle of equal altitudes, or an arc of such a circumference, must be drawn on the inap for use in finding position. For assistance in the delineation of the additional circumference, or arc, the tem late shown in Figure 7 has been provided. his template is made preferably of celluloid, or some other trans arent material. It has a centering indication 10 and a plurality of arcuate slots 11 concentric to indication 10. The slots are graduated in minutes of arcineasure and are adapted to receive and guide the point of a pencil, or other markitu instrument.

ln using the tem late, the centering indiknown position on the map, and that slot which is spaced from indication 10 a distance re resenting the altitude diiierence determine in solving the problem is used as a guide in drawing the desired arc.

There is another feature of the invention which should be considered. The graphical diagram of Figure (i is shown separate from the main chart hearing the map. It is to be understood, however. that the graphical diagram is preferably delineated on an integral part of the chart in lieu of the tables 7.

his construction could not be shown in the accompanyin drawings, due to the limited space availab e on each sheet, so the graphical diagram had to form the subject of a separate figure of drawing.

I claim:

1. An astronomical position-finding chart bearing a representation of a geographical area, and means for indicating azimuth with respect to a known position on the said representation. i

2. An astronomical position-finding chart bearing a re i'esentation of a geographical area, means or indicating azimuth with respect to a known position on the said representatio'n, and means for indicating altitude-dierencesradially with respect to the known position.

3. An astronomical position-finding chart bearing a representation of a geographical area, and a compass diagram overlying the in registration with a said representation with its center coincident with a known positlon thereon.

4. An astronomical position-finding chart bearing a representation of a geographical area, a compass diagram overlying the said representation with its center coincident with a known position thereon, and means Jfor indicating altitude-differences radially with respect to the known position.

5. An astronomical position-finding chart hearing a representation of a geographical area, a compass diagram overlying the said representation with its center coincident with a known position thereon, and circles of equal altitude delineated on the compass diagram concentric thereto.

6. An astronomical position-iinding chart bearing a representation of a eo raphical area, and circles of equal altitu e c elineated on the said representation concentric to a known position thereon,

7. An astronomical position-finding chart bearing a representation of a eographical area, circles of equal altitude elineated on the said representation concentric to a known position thereon, and means for indieating azimuth with respect to theA said known position.

8. The combination with an astronomical position-finding chart bearing a representation of a geogra hical area, of means for indicating azimut with respect to a known position on the said representation and meansy for determining the value of the altitude and of the azimuth that a celestial bod would have in the known position at pre etermined instants of time.

9. The combination with an astronomical position-finding chart bearing a representation of a. geographical area, of means for` indicating altitude ditl'erences radiall with respect to a known position on the said re resentation, an means for determining t e value of the altitude and of the azimuth that a celestial body would have in the known position at predetermined instants of time.

10. The combination with an astronomical position-nding chart bearing a representation of a geogra hical area,of means for indicating azimut with respect to Aa known positionV on the said re resentation, means for indicating altitude-diiierences radially with res ect to the known position, and means for d altitude and of the azimut that a celestial body would have measured in the known position at predetermined instants of time.

11. The combination with an astronomical position-finding chart bearing -a representation of a geographical area, a coinpass dia ram'overlying the said representation wit its center coincident with a known ing the value of the altitude and'of the azieterminin the value of the area, means for indicating muth that a .celestial body would have in the known position at predetermined instants of time.

12. The combination with an astronomical position-linding chart bearing a representation of a geographical area, a plurality of circles of equal altitude delineated on the said representation concentric to a known position thereon, and means for determining the value of the altitude and of the azimuth that a celestial body would have in the known position at predetermined instants of time.

13. The combination with an astronomical position-finding chart bearing a representa tion of a geographical area, a compass diagram overlying the said representation with itscenter coincident with a known position thereon, a plurality of circles of equal altitude delineated on the said representation concentric to the known position, and means for determining the value of the altitude and of the azimuth that a celestial body would have in the known position at predetermined vinstants of time.

14. An astronomical position-finding chart bearing a representation of a geographical azimuth with respect to a known position on the said representation, and a record of the altitudes and azimuths of a celestial body measuredy at the known position at predetermined instants of time.

15. An astronomical position-finding chart bearing a representation of a geographical area, means for indicating altitude differences in a radial direction with respect to a own position on the. said representation, and a record of the of a celestial body measured at the known position at predetermined instants of time.

16. An astronomical position-finding chart a` geographical hearing a representation cf azimuth with measured at the known position time.

17. An astronomical position-finding chart bearing a representation of a geographical means for indicating azimuth with respect to a known position on the said re resentation, and a diagram graphically indicatin altitudes and azimuths of a celestial bo y measured at the known position at predetermined instants of time.

18. An astronomical position-Ending chart bearing a representation of a. geographical arca, a compass' diagram overlying the said representation with its center coincident with a known position thereon and graduated in degrees of azimuth, and a plurality of circles of equal altitude delineated on the said representation concentric to the known position.

19. An astronomical position-linding chart bearing a representation of l concentric to the own position, and a record ofthe altitudes and aziniuths of a celestial body measured at the known position at predetermined instants of time.

In testimony whereof I have allixed my signature.

GEORGE W. LITTLEHALES.

position on the said re muth that a celestial body would have in the known position at predetermined instants `of time.

12. The combination with an astronomical position-finding chart bearing a representation of a geographical area, a plurality of circles of equal altitude delineated on the said representation concentric to aknown position thereon, and means for determining the value of the altitude and of the azimuth that a celestial body would have in the known position at predetermined instants of time.

' 13. The combination with an astronomical position-finding chart bearing a representation of a geographical area, a compass diaam overlying the said representation with its-center coincident with a known position thereon, a plurality of circles of equal altitude delineated on the said representation concentric to the known position, and means for determining the value of the altitude and of the azimuth that a celestial body would have in the known position at predeterminedinstants of time.

14. An astronomical position-finding chart bearing a representation of a geographical area, means for indicating azimuth with respect to a known position on the said representation, and a record of the altitudes and azimuths of a. celestial body measured at the known position at predetermined instants of time.

15. An astronomical position-finding chart bearing a. representation of a geographical area, means for indicating altitude differences in a radial direction with respect to a known position on the said representation, and a record of the altitudes and azimuths of a celestial body measured at the known position at predetermined instants of time.

16. An astronomical position-finding chart bearing a representation of a geographical area, means for indicating azimuth with respect to a known position on the said representation, means for indicatin altitudedifferences in a radial direction wlth respect to the known position, and a record of the altitudes and azimuths of a celestial body measured at the known position at predetermined instants of time.

17. An astronomical position-finding chart bearing a representation of a geographical area, means :for indicating azimuth with respect to a known position on the said representation, and a diagram graphically indicatin altitudes and azimuths of a celestial bo y measured at the known position at predetermined instants of time.

18. An astronomical position-finding chart bearing a representation of a geographical arca, a compassA diagram overlying the said representation with its center coincident with a known position thereon and graduated in degrees of azimuth, and a plurality of circles of equal altitude delineated on the said representation concentric to the known position.

19. An astronomical position-finding chart bearing a representation of a geographical area, a compass diagram overlying the said representation with its center coincident with a known position thereon and graduated in degrees of azimuth, a plurality of circles of equal altitude delineated on the said representation concentric to the known position, and a record of the altitudes and azimuths of a celestial body measured at the known position at predetermined inI stants of time.

In testimony whereof I have affixed my signature.

GEORGE W. LITTLEHALES.

Certicate of Correction.

It is hereby certified that in Letters Patent No. 1,557,854,

anted October 20,

1925, upon the application of George W. Littlehales, of VVasiington.' District of Columbia, for an improvement in Methods and Means for Finding Geographical Posltxon in Navi ation, errors appear in Ythe printed specification requiring correction as follows harz and insert instead,-

age 4, line 65, Strike out the equation (4)- ha'v(90-d) Moda-d) hav(180 [L +d])-hav(L- d) page 5, line 99, before 12 36 insert the sign; .elit should be read with these corrections therein t at record of the case in the Patent Otlice.

and that the said Letters Patthe same may conform to the Signed and sealed this 19th day of January, A. D. 1926.

[emu] WM. A. KINNAN, Acting Qommzsaz'oner of Patents.

Certificate of Correction.

It is hereb certified that in Letters Patent No. 1,557,854, ant/ed October 20, 1925, upon t e application of George W. Lttleliales, of lvasiington.' District of Columbia, for an improvement in Methods and Means for Finding Geographical Position in Navi tion, errors appear in the printed specification requiring correction as follows: age 4, line 65, strike out the equation (4)- and insert instead- M Z Juw(90-d) Imm-h) 4 "Mv(1so-[L+h1)-Mv L-h) page 5, line 99, before 12 36 insert the si and that the said Letters Patexit should be read with these corrections therein t at the same may conform to the record of the case in the Patent Oce.

Signed and sealed this 19th day of January, A. D. 1926.

[sun] WM. A. KINNAN,

Acting Commissioner of Patents.` 

